A note on Wick products and the fractional Black-Scholes model

In some recent papers (Elliott and van der Hoek 2003; Hu and Øksendal 2003) a fractional Black-Scholes model has been proposed as an improvement of the classical Black-Scholes model (see also Benth 2003; Biagini et al. 2002; Biagini and Øksendal 2004). Common to these fractional Black-Scholes models is that the driving Brownian motion is replaced by a fractional Brownian motion and that the Itô integral is replaced by the Wick integral, and proofs have been presented that these fractional Black-Scholes models are free of arbitrage. These results on absence of arbitrage complelety contradict a number of earlier results in the literature which prove that the fractional Black-Scholes model (and related models) will in fact admit arbitrage. The objective of the present paper is to resolve this contradiction by pointing out that the definition of the self-financing trading strategies and/or the definition of the value of a portfolio used in the above papers does not have a reasonable economic interpretation, and thus that the results in these papers are not economically meaningful. In particular we show that in the framework of Elliott and van der Hoek 2003, a naive buy-and-hold strategy does not in general qualify as self-financing. We also show that in Hu and Øksendal 2003, a portfolio consisting of a positive number of shares of a stock with a positive price may, with positive probability, have a negative value.Received: August 2004, Mathematics Subject Classification (2000): 91B28, 60H05JEL Classification: G10Support of the first author from the Jan Wallander and Tom Hedelius foundation is gratefully acknowledged. The research of the second author is supported by the Swedish Research Council.     

Company Tax Structure and Company Tax Incidence

This paper reviews conflicting theories of company tax incidence impliedby the alternative new and traditional views of dividends andexamines their contrasting policy implications. Whereas, under thetraditional view, closer integration of the corporate and personalincome tax systems is suggested, an alternative policy orientationemphasizing the non-distorting features of the classical system is impliedby the new view. Even if the traditional view is accepted, theimplications for design and reform of the company tax vary widely underalternative specifications of domestic and international tax policy objectives. Schedular alternatives to global income taxation are alsoconsidered.     

The impact of settlement period on sales price

This study is an empirical investigation of the impact of settlement period on sales price while controlling for marketing period and standard explanatory variables. The hypothesized positive relationship between settlement period and sales price is confirmed by the results of this study. The estimated coefficient on settlement period is 0.0008 meaning that our market, on average, exacts a premium of 0.08 percent per day of settlement period beyond a norm of 60 days. The estimated coefficient on marketing period (a control variable) is –0.0003 meaning that our market, on average, requires a discount of 0.03 percent per day of marketing period. Our findings show the relative importance of settlement period in making real estate pricing decisions.     

A New Approach to Group Structure, Burden Sharing, and the Equilibrium Provision of Public Goods

In the received model of the voluntary provision of a pure public good, the usual practice is to proceed from assumptions about the group characteristics to inferences about an implied outcome. The approach advocated in this paper reverses the traditional direction. Assuming a Nash equilibrium, we ask how to characterize the diverse set of group characteristics which will support it. Approaching the problem from this angle we define three crucial characteristics of a group-equilibrium: consumer's free rider inducing supply, zero contribution-inducing wealth and voluntary surplus tribute which is the amount by which a person's actual income exceeds his/her zero-contribution inducing wealth. Defining these indicators we show how they form the foundation of a complete mapping between the distribution of individual characteristics of a group, and equilibrium public good supply. Certain questions such as the interaction between size of the group and heterogeneity of incomes and tastes not yet adequately addressed are shown to yield easily to this approach.     

Diversity and relative arbitrage in equity markets

An equity market is called diverse if no single stock is ever allowed to dominate the entire market in terms of relative capitalization. In the context of the standard Itô-process model initiated by Samuelson (1965) we formulate this property (and the allied, successively weaker notions of weak diversity and asymptotic weak diversity) in precise terms. We show that diversity is possible to achieve, but delicate. Several examples are provided which illustrate these notions and show that weakly-diverse markets contain relative arbitrage opportunities: it is possible to outperform or underperform such markets over any given time-horizon. The existence of this type of relative arbitrage does not interfere with the development of contingent claim valuation, and has consequences for the pricing of long-term warrants and for put-call parity. Several open questions are suggested for further study.Received: January 2004, Mathematics Subject Classification (2000): 60H10, 91B28; 60J55JEL Classification: G10We are grateful for the helpful remarks offered by seminar audiences at Columbia, Yale, Princeton, the Sloan School of MIT, Boston University, the Mathematical Institute in Oberwolfach, and the Universities of Athens, Connecticut/Storrs and Texas/Austin. Special thanks go to Professors Jérôme Detemple, Julien Hugonnier, Ralf Korn, Andrew Lo, Mark Lowenstein and Steven Shreve. We are also indebted to Dr. Adrian Banner for a number of discussions that helped sharpen our thinking about these problems, and to the referees and editors for suggestions that improved the exposition. A significant part of this work was completed in the spring semester of 2002, while the second author was on sabbatical leave at the Cowles Foundation for Research in Economics, Yale University. He is grateful to the Foundation for its hospitality.     

Optimal Consumption Taxes and Social Security Under Tax Measurement Problems and Uncertainty

A representative individual lives for two periods; works when young and depends on savings and a government operated social security system when old—the returns on both sources of income, when old, are random. Due to administrative problems the returns to savings are observed with some measurement error. Two alternative consumption tax systems are considered; the Registered Asset Treatment (RAT) and the Non-Registered Asset Treatment (NRAT). The advantage of the RAT is that it can perform a social insurance role while the disadvantage is that it imposes measurement error risk. Correlation between the random return on saving and its measurement error can provide a risk-hedging role that can be further strengthened by the RAT version. The NRAT version neither provides social insurance nor imposes measurement error risk. Both tax systems hedge against the uncertainties in the social security system. The taxpayer engages in precautionary saving in response to future uncertainty.     

The “Rent-To-Own” mortgage and prepayment risk

The most important risk factor in the mortgage and mortgage-backed security market has been prepayment risk. Various innovations have arisen to deal with it but none hedge it fully. The Rent-To-Own (RTO) mortgage discussed here is a mortgage instrument that reduces or even reverses prepayment risk. It does so by creating an incentive structure within the framework of the mortgage contract that penalizes prepayment when interest rates are low and rewards it when interest rates are high. This is the opposite of standard mortgages. The RTO incentive structure is based on a unique buyout feature. Borrowers who want to buy out the financial interest of the lender may do so whenever they want, but the buyout price is a negative function of the market interest rates prevailing currently, that is, at the time of the buyout. Hence the lower these rates, the higher the buyout price. Other advantages of the RTO mortgage are also described.     

The Market for Corporate Control and the Agency Paradigm

The paper analyzes the role of agency driven takeover activity. The analysis shows that takeovers can play an important role in reducing agency costs even though the gains from the corporate restructuring that follows the takeovers are zero, which counters existing models of agency driven takeover activity. The model can therefore form the basis for deriving empirical predictions which discriminate between the agency paradigm and the corporate restructuring paradigm of takeover activity. Negative post-merger performance (Agrawal et al., 1992), which is inconsistent with corporate restructuring is consistent with this model, and that takeover targets' investment levels are below or at the average (Servaes 1994), which is inconsistent with the free cash flow theory is also consistent with this model.     

“Investor sentiment” and the closed-end fund puzzle: A 7 percent solution

Lee, Shleifer, and Thaler (1991) argue that the irrational noise trader model of DeLong, Shleifer, Summers, and Waldmann (1990) ... is consistent with the published evidence on closed-end fund prices. ... However, Lee, Shleifer, and Thaler provide no indication of how much of the variability of a closed-end fund's discounts and premiums is due to such investor sentiment. Using the signal extraction technique of French and Roll (1986) to measure noise, this article estimates that on average only 7 percent of the variance of a standardized measure of weekly changes in discounts and premiums can be attributed to noise-trading activity. Investor sentiment, therefore, seems to account for very little of a closed-end fund's discount and premium variability over time.     

Why Are Earnings Kinky? An Examination of the Earnings Management Explanation

Prior research has documented a kink in the earnings distribution: too few firms report small losses, too many firms report small profits. We investigate whether boosting of discretionary accruals to report a small profit is a reasonable explanation for this kink. Overall, we are unable to confirm that boosting of discretionary accruals is the key driver of the kink. We caution the use of the ratio of small profit firms to small loss firms as a measure of earnings management. We investigate and discuss a number of alternative explanations for the kink.     

Bank lending ‘manias’ in theory and history

A popular view of banking crises sees them as consequences of prior bank lending manias. Such manias are supposed to be especially likely in legally unrestricted banking systems, where banks can issue notes and are not subject to statutory reserve requirements. Here it is argued that the bank lending mania hypothesis (1) exaggerates the role of subjective factors, including bankers' confidence or optimism, as a stimulus to bank lending, and (2) is not supported by evidence from past, legally unrestricted banking systems.     

Computing a Multivariate Normal Integral for Valuing Compound Real Options

We extend the Geske (1979) model to a multivariate normal integral for the valuation of a compound real option. We compared the computing speeds and errors of three numerical integration methods, namely, Drezner's improved Gauss quadrature method, Monte Carlo method and Lattice method, together with appropriate critical value finding methods. It is found that secant method for finding critical values combined with Lattice method and run by Fortran took merely one second, Monte Carlo method 120 seconds. It is also found that the real option decreases with interest rate, not necessarily positively correlated with volatility , a result different from that anticipated under financial option theory. This is mainly because the underlying of real option is a non-traded asset, which brings dividend-like yield into the formula of compound real options. Dividend-like yield rises with the multiplication of correlation coefficient and . High indicates the poor diversification advantage of the new investment project in relation to the existing market portfolio, and the value of real call option decreases with . Conversely, when is low, the proposed project provides better diversification advantage and the real call option rises with . Irrespective of the value of , when interest rate increases, the value of real call option drops, especially when is high, the value of the project is dominated by interest rate.     

Commodity Taxation and Social Welfare: The Generalized Ramsey Rule

Commodity taxes have three distinct roles: (1) revenue collection, (2) interpersonal redistribution, and (3) resource allocation. The paper presents an integrated treatment of these three concerns in a second-best general equilibrium framework, which leads to the generalized Ramsey rule for optimum taxation. We show how many standard results on optimum taxation and tax reform have a straightforward counterpart in this general framework. Using this framework, we also try to clarify the notion of deadweight loss, as well as the relation between alternative distributional assumptions and the structure of optimum taxes.     

What is the Truth About the Scale of Japanese Banks' Bad Debts? Is the Situation Manageable?

In January 1998, the Japanese Ministry of Finance (MoF, 1998) released figures which suggested that the Japanese banking industry';s bad debts might be as high as ¥77 trillion (since revised upward to ¥87.5 trillion, if cooperative-type institutions are included; Financial Supervisory Agency (FSA), 1998). This compared with the previous official estimate of ¥28 trillion. The revelation was designed to do three things: (1) to convince investors, at home and abroad, who had long suspected that the true level of bad debts was much higher than the authorities (and the banks) were willing to admit to, that the authorities were sincere in their quest to enhance disclosure by local financial intermediaries; (2) to stifle opposition to the government's plans to use up to ¥30 trillion (since increased to ¥60 trillion) of public funds to stabilize the financial system¹ by underlining the gravity of the situation facing the Japanese economy; and (3) to pave the way for the introduction of more transparent reporting by the banks in April 1998 when a regime of prompt corrective action (PCA)² was scheduled to commence. This article explains the evolution of bad debt disclosure by the Japanese banking industry and assesses the significance of the latest figures. In particular, it highlights the extent to which accounting forbearance has been, and continues to be, used to mask the true level of the banks' bad debts and refutes the claim that the industry's bad debt burden peaked in 1995. The banking industry's ability to handle the continuing bad debt problem, in the face of a significant impairment of economic capital and the market's relentless drive for full disclosure and transparency, also is assessed.     

A General Theorem on the Comparative Statics of Changes in Risk

In this paper, the concept of absolutely riskier than is introduced to generalize Gollier's (Journal of Economic Theory, 66, 522–535) necessary and sufficient conditions for the comparative statics of a change in risk for risk averters. The restrictive assumption that the payoff function is monotonic in the risk is relaxed. The policymaker's choice problem, the newsboy problem, and a farmer's example are used to illustrate how easily the monotonicity assumption is violated. Finally, some important properties of the concept of absolutely riskier than, such as its relation with the concept of second-order stochastic dominance, are illustrated using the farmer's example.     

On Transitory Earnings

The paper develops a concept of transitory earnings and contrasts this source of earnings to core (or recurring) earnings. It is shown that any two of the following three attributes of transitory earnings imply the third: (i) forecasting irrelevance with respect to next-period aggregate earnings, (ii) value irrelevance, and (iii) unpredictability. The paper makes the case that the current dirty surplus items make sense, especially if one expands the valuation perspective to also allow for agency considerations.     

The origin principle and the welfare gains from indirect tax harmonization

This paper establishes a parallelism between indirect tax harmonization when taxes are levied according to the destination principle and its counterpart when taxes are imposed on an origin basis. Using a simple two-country model of international trade it is argued that, under normal circumstances, indirect tax harmonization under the origin principle, considered as a movement of domestic taxes toward an appropriately designed average tax structure, is potentially Pareto improving. It is also shown that if the initial position is a Nash equilibrium, there are exceptional situations under which the above-mentioned reform may generate an actual Pareto improvement, so that both countries improve their welfare without any need for a compensating international transfer.     

Economic Effects of the 2003 Partial Integration Proposal in the United States

On January 7, 2003, President George W. Bush proposed a significant change in capital income taxation in the United States. In the context of a jobs and growth package, the President proposed to reduce substantially the double taxation of corporate-source income by eliminating investor-level taxes on dividends paid from earnings on which corporate tax had been paid. In addition, the Presidents proposal would have reduced the tax on retained earnings by allowing a basis adjustment for accumulated previously taxed retained earnings. Taken together, these proposals would have moved the U.S. income tax much closer to an integrated tax system along the lines outlined by the Treasury Department in President George H.W. Bushs administration a decade earlier.Putting together the impacts of the Presidents proposal on economic activity through greater capital accumulation and improved calculation, I estimate that the proposal, if it had been enacted in its original form, would yield a permanent increase of 0.48 percent in the U.S. economys potential output. This estimated gain does not include any gains made possible by improved corporate financial policy.At the time of the integration proposal, the author was Chairman of the Council of Economic Advisers.     

Corporate Real Estate and Stock Market Performance

An interesting question in corporate real estate literature is whether real estate can improve the stock market performance of property-intensive non-real estate firms. Using a data set comprising 75 non-real estate corporations that own at least 20 percent properties, this paper empirically assesses and compares the pair-wise return, total risk, systematic risk and Jensen abnormal return performance of composite (with real estate) and hypothetical business (without real estate) firms. We employed Morgan Stanley Capital International world equity index instead of a local market index to provide some insights into the performance of the local market relative to the global market during the 1997–2001 volatile periods experienced by many Asian countries. Our results suggest the inclusion of real estate in a corporate portfolio appears to be associated with lower return, higher total risk, higher systematic risk and poorer abnormal return performance. It is therefore likely that non-real estate firms own properties for other reasons in addition to seeking improvement in their stock market performance. Further research is needed to explore the main factors contributing to corporate real estate ownership by non-real estate firms.     

Restructuring Financial Regulation in the European Monetary Union

This article argues that present financial regulatory arrangements within the European Monetary Union are not adequate either to preserve stability or to foster financial integration. Reform of financial regulation should concentrate on establishing clear procedures for crisis lending and management, with the European Central Bank at the center; preparing the ground for more centralized supervisory arrangements in banking, insurance, and securities; and establishing and consolidating an active domestic and European Union-wide competition policy that limits local market power and national champions that are too big to fail.